I have an impulse response of an LTI system which is
h(n)= n*u(n)-u(n-2) where n=[0,3] (1)
Now regarding the stability and causality of this system, i've drawn the conclusion that the system is causal since the output only relies on past or present values of n and it is stable since n is bounded. In this case n=0,1,2,3. Correct me here if i'm wrong but in case h(n) was u(n) - u(n-2) without knowing anything about n, it would stil be stable right? And if h(n) is the same as the original (1) but again without knowing anything about n it would be unstable correct?
Now i want to analyze this h(n) in odd and even components and also find the linear difference equation of h(n) ,but i can't find anything in my textbook that is of any help. It's the first time i've attended a signals and systems course and i'm really struggling to understand a few things, so any help here would be greatly appreciated.